On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author

Original languageEnglish
Pages (from-to)129-167
Number of pages39
JournalGeophysical and Astrophysical Fluid Dynamics
Volume16
Issue number1-2
Publication statusPublished - 1980

Fingerprint

spherical shells
shell
Fluids
Gravity waves
propagation
fluid
inner core
Prandtl number
heat source
gravity wave
transform
convection
oscillation
axes of rotation
radii
touch
fluids
free vibration
equators
gravity waves

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Space and Planetary Science
  • Computational Mechanics
  • Mechanics of Materials
  • Astronomy and Astrophysics

Cite this

@article{6298c20c751c4c52be48d36515dd2e60,
title = "On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.",
abstract = "The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author",
author = "Eltayeb, {I. A.}",
year = "1980",
language = "English",
volume = "16",
pages = "129--167",
journal = "Geophysical and Astrophysical Fluid Dynamics",
issn = "0309-1929",
publisher = "Taylor and Francis Ltd.",
number = "1-2",

}

TY - JOUR

T1 - On the propagation and stability of wave motions in rapidly rotating spherical shells. I. the non-magnetic case.

AU - Eltayeb, I. A.

PY - 1980

Y1 - 1980

N2 - The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author

AB - The linear propagation properties of wave motions in a rapidly rotating stratified Boussinesq spherical shell, of outer radius 1 and inner radius eta, are studied in the small Prandtl number limit. When eta = O, the various possible motions can be accommodated in two classes: F and D. The class F is closely related to the class of free oscillations of the inviscid unstratified fluid shell while D corresponds to diffusive inertial-gravity waves. Both F and D are subdivided into two infinite sets of modes one of which (E) is symmetric and the other (O) is anti-symmetric about the equatorial plane. The sets E and O for class F are further subdivided into two infinite subsets one of which propagates (in phase) eastward and the other westward. Waves of class D propagate eastward. The two classes F and D are decoupled except for one mode which belongs to D on and in the immediate neighbourhood of the axis of rotation and transforms into F away from the axis. This mode provided the already known mode of convection of the linear stability of a fluid sphere containing a uniform distribution of heat sources. When an inner solid core is present (and eta is non-zero) all the modes of classes F and D persist outside Cc (where Cc is the coaxial cylinder whose generators touch the inner core at its equator) but the set E of modes (of both F and D) is suppressed within Cc.-Author

UR - http://www.scopus.com/inward/record.url?scp=0019193609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019193609&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0019193609

VL - 16

SP - 129

EP - 167

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 1-2

ER -